Solving the Mystery: Understanding Relativity in a Simple Race

[abbott287]

What is wrong here? thanks for any help.

On earth, a race is set up between 2 cars and a light beam. The starting line is drawn, and the two cars are adjusted behind that line and get a jump start. This is done so that one car will be traveling 100 MPH when it hits the starting line, and the other 20 MPH. Both cars will stay at those exact speeds. When both cars hit the starting line (at the exact same time) the light beam will be set off as well. The race will last exactly one second. Both cars are equipped with special measuring devices to measue the speed of the light beam during the one second race. OK get ready, get set..GO! Tick,tock...Done! That light beam was fast! It traveled 186,000 miles in that second! The car going 100 MPH traveled .027 miles, and the car traveling 20 MPH went only .005 miles. Both cars measuerd the speed of light during the race, and both found that the beam of light was moving away from them at 186,000 miles per second. At that rate, when the race was over (one second), It seems the light beam should be 186K miles ahead of both cars finishing points, but also 186K miles from the starting line. However, that would give three separate distances. When measured after the race, the light beam was actually the proper distance from the starting line. (186 K miles.) It seems to me after the race, the light beam would only be 186K miles minus .027 miles in front of the 100MPH car, and 186K miles minus .005 Miles in front of the 20 MPH car. What am I missing? Thanks for any help setting me straight on this.

 

[DaveC426913]

What you're missing is that the two cars do not measure the passage of time the same.

Since one is moving faster than the other, it is just slightly more relativistically time dilated - his clock ticks slightly slower - meaning that second is not up yet. When the second is up for that faster car, he will have measured light to have moved 186,000 miles.

 

[abbott287]

What you're missing is that the two cars do not measure the passage of time the same.

Since one is moving faster than the other, it is just slightly more relativistically time dilated - his clock ticks slightly slower - meaning that second is not up yet. When the second is up for that faster car, he will have measured light to have moved 186,000 miles.

The cars measured the speed the light was moving away from them only. (c) The distances were measured after the race was over. The race was stopped after one second on a bystanders watch. The light beam had moved 186K miles from the start line. (Which it should have) The two cars were closer than that, although they both measured C for the speed of light.. Are you saying the measuring devices on the cars were slower due to their speed, even though it was so low? If so, I take it that is the answer I was looking for!

 

[DaveC426913]

Are you saying the measuring devices on the cars were slower due to their speed, even though it was so low?

Yep.

It is a tiny difference, true, but then again .027 miles is a tiny fraction of 186,000 miles, isn't it?

 

[abbott287]

Perfect and simple. Thank you for taking the time to answer my problem. :)